October 2026 TEAS 7 Mathematics Study Guide

Fractions and decimals Adding and subtracting fractions needs a common denominator; multiplying does not. To compare fractions quickly, cross-multiply rather than converting both to decimals. Read the full guide Multiply and divide fractions Multiply straight across, numerator by numerator and denominator by denominator. To divide, invert the second fraction and multiply. This is the rule usually remembered as "keep, change, flip". Read the full guide Converting fractions into decimals Divide the numerator by the denominator. Knowing the common conversions on sight, including 1/2, 1/3, 1/4, 1/5, 1/8 and their multiples, saves time you will need elsewhere. Read the full guide Percent and decimals A percentage is a fraction of 100, so 45% is 0.45. To find a percentage of a number, multiply; to find what percentage one number is of another, divide the part by the whole and multiply by 100. Read the full guide Proportions A proportion sets two ratios equal and is solved by cross-multiplying. This is the single most useful skill on the section, because dosage, scale and unit problems are all proportions in disguise. Read the full guide Absolute change and relative change Absolute change is the raw difference between two values. Relative change expresses that difference as a percentage of the starting value, which is why a small absolute change can be a large relative one. Read the full guide Variables and equations Solve by isolating the variable, doing the same operation to both sides and undoing operations in reverse order. Substitute your answer back into the original equation to check. Read the full guide Dependent and independent variables The independent variable is the one that is changed or controlled; the dependent variable is the one measured in response. On a graph the independent variable goes on the x-axis. Read the full guide Application of slope Slope is rise over run: the change in y divided by the change in x. In a word problem it is a rate, such as cost per item, distance per hour, or dose per kilogram. Read the full guide Money management Budgeting questions cover income against expenses, unit price comparison, discounts, tax, tips and simple interest. They are multi-step arithmetic problems presented in a real context. Read the full guide

Measurements and units You need household and metric conversions and the relationships between them: 1 kg is about 2.2 lb, 1 inch is 2.54 cm, 1 L is about 1.06 quarts. Convert in single, checkable steps. Read the full guide Identifying appropriate units of measurement Choosing a sensible unit is its own skill: millilitres for medication, litres for fluid intake, grams for a dressing, kilograms for a patient. The answer is the unit that gives a manageable number. Read the full guide Visualizing data Bar charts compare categories, line graphs show change over time, pie charts show parts of a whole, and scatter plots show relationships between two variables. Match the display to the question being asked. Read the full guide Statistics Mean is the average, median the middle value of an ordered list, mode the most frequent, and range the highest minus the lowest. Median resists outliers where mean does not. Read the full guide Probability Probability is favourable outcomes over total outcomes, expressed as a fraction, decimal or percentage between 0 and 1. For independent events happening together, multiply the separate probabilities. Read the full guide Area of geometric figures Rectangle is length × width, triangle is half base × height, parallelogram is base × height. Composite shapes are solved by splitting them into these and adding. Read the full guide Circumference and area of a circle Circumference is 2πr and area is πr². The commonest slip is being given a diameter and using it as the radius, which doubles or quadruples the answer. Read the full guide Sides of a right-triangle The Pythagorean theorem, a² + b² = c², relates the two shorter sides to the hypotenuse. The hypotenuse is always the longest side and always opposite the right angle. Read the full guide